Asymptotic bound for equiangular lines with angle arccos 1/(2r-1)

Let $N_{1/(2r-1)}(d)$ denote the maximum number of equiangular lines in $\mathbb{R}^d$ with common angle $\arccos \frac{1}{2r-1}$, where $r\geq 2$ is an integer. Asymptotic equiangular-lines conjecture. For every integer $r\geq 2$,

$$N_{1/(2r-1)}(d)=\frac{r}{r-1}d+O(1)$$

as $d$ tends to infinity. The construction preceding the conjecture gives the matching lower bound, and the cited results suggest that it is sharp; the conjectured asymptotic upper bound remains open.